04/19/23 PH 105

5

0.1

Problem on uniform acceleration (from Ch. 2):A bike moving at constant velocity 5 m/s passes a car stopped at a light, as the light turns green and the car begins to accelerate at 2 m/s2.(a) When does the car pass the bike (in sec.)?

PH 105-003/4 ---- Friday, Aug. 22, 2007

Equationsvf = vi + a txf = xi + vi t + ½ a t2

04/19/23 PH 105

A. 10 m from light

B. 15 m

C. 20 m

D. 25 m

E. 40 m

F. 50 m

A bike moving at constant velocity 5 m/s passes a car stopped at a light, as the light turns green and the car begins to accelerate at 2 m/s2.(a) When does the car pass the bike?

Equationsvf = vi + a txf = xi + vi t + ½ a t2

(b) Where does this happen?

04/19/23 PH 105

Problem on uniform acceleration:A bike moving at constant velocity 5 m/s passes a car stopped at a light, as the light turns green and the car begins to accelerate at 2 m/s2.(a) When does the car pass the bike?(b) Where does this happen?

A. EquationsB. vf = vi + a tC. xf = xi + vi t + ½ a t2

(c) How fast is the car moving then (in m/s)?

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0.1

04/19/23 PH 105

Components of a Vector• A component is a

projection of a vector along an axis– Any vector can be

completely described by its components

• It is useful to use rectangular components– These are the projections

of the vector along the x- and y-axes

PH 105-003/4Friday, Aug. 29, 2007

04/19/23 PH 105

Math Review

Trigonometry

ca

b

sin = a/c, cos = b/ctan = a/b

c2 =a2 + b2 (Pythagorean Theorem)

Example: V

V = 785 km/h, find Vx and Vy

vy

VxVx = Vsin = 489 km/hVy = Vcos = 614 km/hCHECK: 7852 = 4892 + 6142

Position and Displacement• The position of an

object is described by its position vector,

• The displacement of the object is defined as the change in its position

•

r

f ir r r

PH 105-003/4Wednesday, September 5, 2007

Instantaneous Velocity• The instantaneous velocity

is the limit of the average velocity as Δt approaches zero

– As the time interval becomes smaller, the direction of the displacement approaches that of the line tangent to the curve

0limt

d

t dt

r rv

Average Acceleration

f i

avgf it t t

v v va

Motion with Uniform Acceleration in 3D

The velocity vector can be obtained from the definition of acceleration:

• The position vector can be expressed as a function of time:

21

2f i it tr r v a

f i tv v a

Simplest case of uniformly-accelerated 2D motion:

Projectile motion (free fall)• a = constant = (0, -g, 0) = -g j

• ax = 0, ay = -g, az = 0

PH 105-003/4Friday, September 7, 2007

vx = vix + ax t x = xi + vix t + ½ ax t2 vy = viy + ay t y = yi + viy t + ½ ay t2

vx = vix (constant) x = xi + vix tvy = viy – gt (NOT const.)y = yi + viy t – ½ g t2

active figure 4.07

Clicker Question The dome light breaks off in a car moving at a constant velocity 30 m/s. It will hit the floor

of the car:

A. Directly under its starting point

B. Behind its starting point

C. Ahead of its starting point

v = 30 m/s

AB C

Assumptions of Projectile Motion

• The free-fall acceleration is constant over the range of the motion– It is directed downward– This is the same as assuming a flat Earth over the

range of the motion– It is reasonable as long as the range is small

compared to the radius of the Earth

• The effect of air friction is negligible• With these assumptions, an object in projectile

motion will follow a parabolic path (y ~ x2)

Sample clicker question (test-taking skills): 40 20

?

A. 0

B. 1

C. 2

D. 3

E. 4

F. 5

G. 6

H. 7

PH 105-003/4 -- Monday, September 10, 2007

04/19/23 PH 105

Sample clicker question (test-taking skills):A man walks 40 meters in 20 seconds. What is his average velocity, in m/s?

A. 0

B. 1

C. 2

D. 3

E. 4

F. 5

G. 6

H. 7

Range of a Projectilevx = vix (constant) x = xi + vix tvy = viy – gt (NOT const.)y = yi + viy t – ½ g t2

means where does it return to y=0?

0 = 0 + viy t – ½ g t2

viy = ½ g t

t = 2viy/gis when, not where!

2 sin2i ivR

g

x = 0 + vix t = 2 vix viy /g= 2 vicos vi sin /g

Range of a Projectile2 sin2i iv

Rg

Uniform Circular Motion• Trajectory is a circle, so

ri = ri = r

• Use definitions of a, v:

v = a t, r = v t• If small,

v ~ v r ~ r so

at~ vr, vt~r Divide: a/v = v/r, or

a = v2 / r

04/19/23 PH 105

Clicker question (vectors)A man walks 30 m north, then 40 m

east. The magnitude of his total displacement is (in m)

A. 10

B. 30

C. 40

D. 50

E. 70

04/19/23 PH 105

Clicker Question: relative motionA UA student is driving (horizontally) 40 m/s in a convertible when 1 cm diameter hail starts to fall, vertically at 30 m/s.The speed with which the hail strikes her is

A. 30 m/s

B. 40 m/s

C. 50 m/s

D. 60 m/s

E. 70 m/s